We derive, using the classical Hamilton-Jacobi theory, exact and general relativistic expressions for the ponderomotive scattering angles of an electron which is incident initially with an arbitrary velocity on the focal region of a laser pulse of arbitrary intensity, polarization, and pulse shape. The result is used to analyze the experimental data recently obtained by Meyerhofer et al. [J. Opt. Sec. Am. B 13, 113 (1996)] and to predict the ponderomotive scattering angles for very high incident energies as envisaged in laser-accelerator experiments.